Wave/Displace Modifier in BGE?
The answer for this is Very simple. Modifiers do not update in the game engine (Only the selected frame will display) and generated textures do not work in the BGE either. What you are trying to do will not work, at least with the current approach you are trying to use. This will obviously work the previewing it in the viewport, because modifiers and generated textures work for Blender Internal, just not the game engine. When you press P, only one frame of your plane with the modifier is displaying. View This question on why modifiers will not update in the game engine.